Answer:
e=-2
Step-by-step explanation:
9e-7e=-11+7
2e=-4
e=-2
In the figure below, if the angle is right what is the value of x?
Answer:
x = 50
Step-by-step explanation:
Since the angle is right = 90°, then
40 + x = 90 ( subtract 40 from both sides )
x = 50
Answer:
[tex]\boxed{\sf x = 50\ degrees}[/tex]
Step-by-step explanation:
x = 90 - 40 [Complementary angles add up to 90 degrees]
x = 50 degrees
Write the expression 12^-2 in simplest form?
Answer:
12 to the power of -2 is 0.00694444444
Step-by-step explanation:
When ever doing a number to the power of a negative number, the result will always be a fraction of a number.
Or
Fraction:
1/12^2
which is
1 / 144
Percentage:
0.00694444444 * 100 = 0.694444444%
Hope this helps, have a good day :)
(brainliest would be appreciated?)
The simplest form of the given expression [tex]12^{-2}[/tex] is 1/144.
The given expression is,
[tex]12^{-2}[/tex]
Here we can see that 12 has inverse power of 2.
Simplify it using basic rules of exponents.
To do so, we need to understand that a negative exponent indicates that the base should be inverted.
In other words, [tex]12^{-2}[/tex] is the same as 1/12²
To simplify this further,
Evaluate 12², which is,
12² = 12 x 12
= 144
Therefore, 1/12² can be expressed as 1/144.
Hence,
In the simplest form, we can write [tex]12^{-2}[/tex] as 1/144.
Learn more about the mathematical expression visit:
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i need help on figuring this out and the answer plz!!
Answer:
$76
Step-by-step explanation:
The amount changed is the total amount of the whole entire thing.
Therefore, we use absolute value or simply find the difference.
21 - (-55) = 76
So the bank account changed $76 over the 2 days.
5. Find the product of p(x) and q(x) if p(x) = 2x+7 and q(x) = 4x-9
a. Is p(x) a polynomial? If not, give an explanation.
b. Is q(x) a polynomiala If not, give an explanation.
c. Is the product a polynomials If not, give an explanation,
d. If the product is a polynomial, identify type and degree.
Answer:
p(x), q(x), and their product are all polynomials.
p(x) · q(x) = 6x² + 10x - 63
Step-by-step explanation:
First of all P(x) and q(x) are polynomials because polynomials refer to any sum, difference, or product of a collection of algebraic terms. The word polynomials is general. P(x) and q(x) are polynomials but more specifically they are binomials since they only have two terms. Their product is a polynomial as well, but more specifically its a trinomial because it has three terms.
process of multiplying
Using the distributive property (or foil method) when multiplying p(x) and q(x) you would first get the expression 6x² - 18x + 28x - 63. From here you would combine "like terms". This would give you your final answer of
6x² + 10x - 63. Sorry, I couldn't help you with the D question but I hope this helps ;)
Type the correct answer in the box. Use numerals instead of words.
Find the sum of the finite geometric series.
Mr. Jamison deposited $100 into a new savings account on January 1. On the first day of each month thereafter, he deposited three times the amount he deposited in the previous month. On June 15 of the same year, the total amount Mr. Jamison has deposited is $
Answer:
$36,400
Step-by-step explanation:
Mr Jamison deposited $100 in January
February=3*100=$300
March=3{3(100)=3^2(100)=9*100=$900
April=3^3(100)=27*100=$2,700
May=3^4(100)=81*100=$8,100
June=3^5(100)=243*100=$24,300
Total amount=$100 + $300 + $900 + $2700 + $8100 + $24300
=$36,400
The total amount deposited by Mr Jamison on June 15 is $36,400
10
Complete the conversion. $2 per pound = $_ per ounce (round to the nearest hundredth)
Answer:
$2 per pound = $0.125. per pound
Step-by-step explanation:
The unit of weight conversion from pound to ounce is given as follows;
1 pound weight = 16 ounces weight
1 ounce weight = 1/16 pound weight
Therefore, whereby the cost of 1 pound weight of an item is two dollars, we have;
The cost of one ounce weight of the item will be the cost of 1 pound weight, divided by 16 and given as follows;
$2 per pound = $2/16 per pound = $0.125. per pound
Therefore;
$2 per pound = $0.125. per pound.
A history professor decides to give a 12-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than 0.10. What score should be set as the lowest passing grade? Group of answer choices
Answer:
we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10
Step-by-step explanation:
From the given information;
Sample size n = 12
the probability of passing a student who guesses on every question is less than 0.10
In a alternative - response question (true/false) question, the probability of answering a question correctly = 1/2 = 0.5
Let X be the random variable that is represent number of correct answers out of 12.
The X [tex]\sim[/tex] BInomial (12, 0.5)
The probability mass function :
[tex]P(X = k) = \dfrac{n!}{k!(n-k)!} \times p^k\times (1-p)^{n-k}[/tex]
[tex]P(X = 12) = \dfrac{12!}{12!(12-12)!} \times 0.5^{12}\times (1-0.5)^{12-12}[/tex]
P(X = 12) = 2.44 × 10⁻⁴
[tex]P(X = 11) = \dfrac{12!}{11!(12-11)!} \times 0.5^{11}\times (1-0.5)^{12-11}[/tex]
P(X =11 ) = 0.00293
[tex]P(X = 10) = \dfrac{12!}{10!(12-10)!} \times 0.5^{10}\times (1-0.5)^{12-10}[/tex]
P(X = 10) = 0.01611
[tex]P(X = 9) = \dfrac{12!}{9!(12-9)!} \times 0.5^{19}\times (1-0.5)^{12-9}[/tex]
P(X = 9) = 0.0537
[tex]P(X = 8) = \dfrac{12!}{8!(12-8)!} \times 0.5^{8}\times (1-0.5)^{12-8}[/tex]
P(X = 8) = 0.12085
[tex]P(X = 7) = \dfrac{12!}{7!(12-7)!} \times 0.5^{7}\times (1-0.5)^{12-7}[/tex]
P(X = 7) = 0.19335
.........
We can see that,a t P(X = 9) , the probability is 0.0537 which less than 0.10 but starting from P(X = 8) downwards the probability is more than 0.01
As such, we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10
Solve |2x+3/4 |=5 1/2 Please help!!!!
Answer:
=2x+3/4=5.50
x=19/8 or 2 3/8
hope this helps
Step-by-step explanation:
Scores on the Mathematics section of the SAT Reasoning Test form a normal distribution with a mean of μ = 500 and a standard deviation of 100. What is the minimum score necessary to be in the top 10% of the distribution?
Answer:
The minimum score necessary to be in the top 10% of the distribution is 628.
Step-by-step explanation:
Given that a normal distribution has a mean of μ = 500 and a standard deviation = σ= 100
The Significance level for this test = 10 % = 0.1
For one tailed test ∝= 0.1 the value of Z∝= ±1.28
Since it a normal distribution the test statistic used is
Z= X= u / σ/√n ( taking n= 1)
1.28 = X- 500/100/√1
128 + 500 = X
or X = 628
The minimum score necessary to be in the top 10% of the distribution is 628.
Which polynomial is a factor of both expressions? x – 8 x + 7 x – 2 (x – 2)2
Answer:
C. x-2
Step-by-step explanation:
edge
Answer: the 3rd the answer c
x-2
Step-by-step explanation:
Use the Law of Sines to find the missing angle of the triangle.
Find m < C to the nearest tenth if the c= 102, a = 71 and m < A=40
Answer:
66.9 degrees
Step-by-step explanation:
The Law of Sines states that a/sinA = c/sinC. Plugging in the values for c, a, and M < A, we get:
71/sin40 = 102/sinC
Cross multiplying, we get:
102(sin40deg) = 71(sinC)
Now, we simplify the left side and get:
65.56 = 71(sinC)
Next, we divide 65.56 by 71 to get:
0.92 = sinC
Taking the inverse sign we get:
C = 66.9 degrees
how to do this question plz answer me step by step plzz plz plz plz plz I really struggling
Answer: 48
There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.
========================================================
1 min = 60 sec
30 min = 1800 sec (multiply both sides by 30)
1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")
The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.
There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.
--------------------
Extra info:
If you're curious about finding the more accurate value, then you could follow these steps
1 prize = 2014 seconds
x prizes = 86400 seconds (number of seconds in a full day)
1/x = 2014/86400
1*86400 = x*2014
86400 = 2014x
2014x = 86400
x = 86400/2014
x = 42.8997020854021
Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.
Help please, I would really appreciate it. :)
Answer:
9, 13, 17, 21
Step-by-step explanation:
If x=2,
y=1+4(2)
y=9
This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.
On a cold February morning, the temperature of the radiator fluid in Stanley’s car is . When the engine is running, the temperature of the fluid goes up per minute. Approximately how long will it take before the radiator fluid temperature reaches ?
Answer:
18.18 min
Step-by-step explanation:
The complete question is
On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?
The initial temperature of the engine [tex]T_{1}[/tex] = -18 F
rate of increase in temperature r = 5.4 F/min
Final temperature [tex]T_{2}[/tex] = 80 F
Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F
time taken to reach this 80 F will be = ΔT/r
where ΔT is the difference in temperature
r is the rate of change of temperature
time taken = 98/5.4 = 18.18 min
find the midpoint of the line segment whose endpoints are
(5,9) (2,-1)?
Answer:
(3.5,4)
Step by step explanation:x coordinate =
[tex] \frac{5 + 2}{2} [/tex]
= 3.5
y coordinate =
[tex] \frac{ - 1 + 9}{2} [/tex]
= 4
midpoint = (3.5,4)
Answer:
( 3.5,4)
Step-by-step explanation:
To find the midpoint
Add the x coordinates together and divide by 2
(5+2)/2 = 7/2 = 3.5
Add the y coordinates together and divide by 2
(9+-1)/2 = 8/2 = 4
( 3.5,4)
One January day, the low temperature in Fargo, ND was -8 degrees. Over a period of six hours, the temperature rose 4 degrees per hour. After
what was the temperature?
hours
O 24 degrees
O 16 degrees
40 degrees
O 32 degrees
Es Review
Answer:
Hey there!
The temperature started at -8 degrees.
The total rise of the temperature was 6(4) or 24 degrees.
-8+24=16
The temperature after 6 hours was 16 degrees.
Let me know if this helps :)
The temperature after 6 hour is 16°. Therefore, option B is the correct answer.
What is temperature?Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.
Given that, One January day, the low temperature in Fargo, ND was -8 degrees.
Over a period of six hours, the temperature rose 4 degrees per hour.
So, total temperature rose in 6 hours is 24 degrees
Temperature after 6 hour is -8+24
= 16°
The temperature after 6 hour is 16°. Therefore, option B is the correct answer.
Learn more about the temperature here:
https://brainly.com/question/11464844.
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I need a lot of help
To add fractions with different denominators you must find the highest common factor (the highest number they both go into).
For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8
now, whatever you do to the bottom, you must do to the top.
So:
3 x 2 = 6 and 5 x 4 = 20
Therefore, your answer would be 6/8 + 20/8
You do that for the rest of them as well, do you get it?
Answer:
3/4 + 5/2 = 3/4 + 10/4 = (3+10)/4 = 13/43. 4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15
5. 2/3 + 7/10 = 20/30 + 21/30 = (20+21)/30 = 41/30
Find the value of x in the given
right triangle.
Enter your answer as a decimal rounded to the
nearest tenth.
Answer:
x = 12.5Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use cosine
cos∅ = adjacent / hypotenuse
From the question
The hypotenuse is x
The adjacent is 10
Substitute these values into the above formula and solve for x
That's
[tex] \cos(37) = \frac{10}{x} [/tex][tex]x \cos(37) = 10[/tex]Divide both sides by cos 37
[tex]x = \frac{10}{ \cos(37) } [/tex]x = 12.52135
We have the final answer as
x = 12.5 to the nearest tenthHope this helps you
Answer:
probably 16.5
Step-by-step explanation:
88 feet/second = 60 miles/hour. How many feet per second is 1 mile? (Hint: divide both side of the equation by the same amount.)
Answer:
1 mile/hour is equivalent to 1.47 feet/seconds
Step-by-step explanation:
Given
[tex]88 ft/s= 60 miles/hr[/tex]
Required
Determine the equivalent of 1 mile/hour
[tex]88\ ft/s= 60\ miles/hr[/tex]
Express 60 as 60 * 1
[tex]88\ ft/s= 60 * 1\ mile/hr[/tex]
Divide both sides by 60
[tex]\frac{88\ ft/s}{60}= \frac{60 * 1\ mile/hr}{60}[/tex]
[tex]\frac{88\ ft/s}{60}= 1\ mile/hr[/tex]
Reorder
[tex]1\ mile/hr = \frac{88\ ft/s}{60}[/tex]
Divide 88 by 60
[tex]1\ mile/hr = 1.46666666667\ ft/s[/tex]
Approximate to 3 significant figures
[tex]1\ mile/hr = 1.47\ ft/s[/tex]
Hence;
1 mile/hour is equivalent to 1.47 feet/seconds
Donald has a bunch of nickels and dimes in his piggy bank. There are 100 coins in the bank that make a total of $6.60 in change. If n is the number of nickels and d is the number of dimes, how many of each type of coin does Donald have?
Answer:
78 nickels and 22 dimes
Step-by-step explanation:
Nickels = n, Dimes = d
Number of coins = 100
n + d = 100Total sum in the piggy bank = $6.60
5n + 10d = 660Consider the first equation in the second:
5(100 -d) + 10d = 660500 - 5d + 10d = 6605d = 110d = 110/5d = 22n = 100 - 22n = 78Answer: nickels 78 and dimes 22
Answer:
78 nikes and dimes 22
solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11
Step-by-step explanation:
A Water flows through a pipe at a rate of 10 milliliters every 8.5 seconds. Express this
rate of flow in liters per minute. Round your answer to the nearest hundredth
Answer:
The answer to the nearest hundredth is 0.07 liters per minute
Step-by-step explanation:
In this question, we are told to express the given metric in liters per minute.
The key to answering this question, is to
have the given measurements in the metric in which we want to have the answer.
Hence, we do this by converting milliliters to liters and seconds to minute.
Let’s start with milliliters;
Mathematically;
1000 milliliters = 1 liters
10 milliliters = x liters
x * 1000 = 10 * 1
x = 10/1000
x = 1/100
x = 0.01 liters
For the seconds;
We need to convert the seconds to minutes;
Mathematically;
60 seconds = 1 minute
8.5 seconds = y minutes
60 * y = 8.5 * 1
y = 8.5/60
y = 0.14167 minutes
Now, our rate of flow is liters per minute, that means we have to divide the volume by the time;
Hence, we have ;
0.01/0.14167 = 0.070588235294
Which to the nearest hundredth is 0.07
construct a right-angled triangle ABC where angle A =90 degree , BC= 4.5cm and AC= 7cm. please ans fast........ Very urgent. Pls don't give wrong answers
Answer and Step-by-step explanation: The described right triangle is in the attachment.
As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:
AC² = AB² + BC²
[tex]AB^{2} = AC^{2}-BC^{2}[/tex]
[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]
[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]
[tex]AB =\sqrt{28.75}[/tex]
AB = 5.4
Then, right triangle ABC measures:
AB = 5.4cm
BC = 4.5cm
AC = 7cm
Below are a list of costs and discounts for groceries. Round to the nearest dollar to estimate the total cost
+ $12.34
+ $5.07
- $0.73
+ $2.84
- $1.50
Answer:
$18
Step-by-step explanation:
$18.02 rounds to $18
Answer:
$17
Step-by-step explanation:
Rounded, the listed numbers are ...
12 + 5 -1 +3 -2 = 17
The estimate of total cost is $17.
Can someone answer this please? Okay so it says that something is made 3 times than the other item. The other item uses 13 beads. So, what is 13 times 3?
Answer:
13x3= 39
Step-by-step explanation:
10x3=30
3x3=9
30+9=39
Hope it helps!
determine if the equation is a linear equation -x + 3y^2=18
Answer:
No
Step-by-step explanation:
Linear equations must have no squares, roots, cubes, or any powers. If the graph has an asymptote or any restrictions, it is not a linear function.
A linear function will only appear in either point-slope form or slope-intercept form. These forms will not have square roots or powers in them.
-x + 3y² = 18
We know here that this is not a linear function. But we can try to write it in slope-intercept form:
3y² = x + 18
y² = x/3 + 6
y = √(x/3 + 6)
We can see from here that our graph is a square root function and has a restricted domain (no negative numbers).
Alternatively, we can graph the equation to see if it is a constant line (linear equation) or not. When we do so, we see that it is definitely not a linear function:
In a previous poll, % of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the significance level.
Answer:
We conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased.
Step-by-step explanation:
The complete question is: In a previous poll, 46% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 480 of 1081 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the [tex]\alpha[/tex] = 0.10 significance level.
Let p = population proportion of families with children under the age of 18 who eat dinner together seven nights a week.
So, Null Hypothesis, : p 46% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remains same}
Alternate Hypothesis, : p < 46% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of families = [tex]\frac{480}{1081}[/tex] = 0.44
n = sample of adults with children under the age of 18 = 1081
So, the test statistics =
= -1.32
The value of z-statistics is -1.32.
Also, the P-value of the test statistics is given by;
P-value = P(Z < -1.32) = 1 - P(Z [tex]\leq[/tex] 1.32)
= 1 - 0.9066 = 0.0934
Since the P-value of our test statistics is less than the level of significance as 0.0934 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased.
Please answer quick Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2. (5 points) y^2 = 4x 8y = x^2 x = 1 divided by 8 y^2 y = 1 divided by 8 x^2
Answer:
Step-by-step explanation:
If you plot the focus and the directrix on a coordinate plane, because the parabola wraps itself around the focus away from the directrix, we know that this parabola opens to the left. That means its general form is
[tex]4p(x-h)=-(y-k)^2[/tex] where h and k are the coordinates of the vertex and p is the distance between the vertex and either the focus or the directrix because both distances are the same. Knowing that both distances are the same, it logically follows that the vertex is directly in between the focus and the directrix. So the vertex is at the origin, (0, 0). p is 2 because the vertex is at an x value of 0 and the directrix is at the x value of 2, and because the focus is at an x value of -2. Filling in the equation, then:
[tex]4(2)(x-0)=-(y-0)^2[/tex] which simplifies to
[tex]8x=-y^2[/tex] and, solving for x:
[tex]x=-\frac{1}{8}y^2[/tex]
a hotel manager wants miriam to tile their lobby using the dame design she created for Mr.Rivera.The lobby measures 45 feet by 45 feet. he wants the outer edge to be the same color as the center tile. will this occur ? justify your answer
Answer:
Yes it will occur
Step-by-step explanation:
The lobby measures 45 feet by 45 feet
Area of the lobby = 45 * 45
=2025 ft^2
So, the lobby has 2025 tiles
subtract 1 black tile in the center
2025 tiles - 1 black tile =2024 tiles
The number of blue tiles and black tiles is 2024 tiles
He wants the outer edge to be the same color as the center tile so, divide by 2
2024/2 = 1012 tiles
The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles
I need help and fast!!!!
Answer:
H. b/a
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Label our variables
y₂ = 2b
y₁ = b
x₂ = 2a
x₁ = a
Step 2: Plug into formula
m = (2b - b)/(2a - a)
Step 3: Evaluate
m = b/a
Answer:
b/a
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1)/(x2-x1)
= ( 2b - b)/ ( 2a -a)
= b/a
The base of a right triangle is increasing at a rate of 2 meters per hour and the height is decreasing at a rate of 3 meters per hour. When the base is 9 meters and the height is 22 meters, then how fast is the HYPOTENUSE changing
Answer:
dL/dt = - 2,019 m/h
Step-by-step explanation:
L² = x² + y² (1) Where x, and y are the legs of the right triangle and L the hypotenuse
If the base of the triangle, let´s call x is increasing at the rate of 2 m/h
then dx/dt = 2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h
If we take differentials on both sides of the equation (1)
2*L*dL/dt = 2*x*dx/dt + 2*y*dy/dt
L*dL/dt = x*dx/dt + y*dy/dt (2)
When the base is 9 and the height is 22 according to equation (1) the hypotenuse is:
L = √ (9)² + (22)² ⇒ L = √565 ⇒ L = 23,77
Therefore we got all the information to get dL/dt .
L*dL/dt = x*dx/dt + y*dy/dt
23,77 * dL/dt = 9*2 + 22* ( - 3)
dL/dt = ( 18 - 66 ) / 23,77
dL/dt = - 2,019 m/h
Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.
The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:
[tex]h^2 = x^2 + y^2[/tex]
In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:
[tex]h^2 = 9^2 + 22^2[/tex]
[tex]h = \sqrt{9^2 + 22^2}[/tex]
[tex]h = 23.77[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
Simplifying by 2:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].
We want to find [tex]\frac{dh}{dt}[/tex], hence:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]
[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]
[tex]\frac{dh}{dt} = -2.02[/tex]
The hypotenuse is changing at a rate of -2.02 meters per hour.
A similar problem is given at https://brainly.com/question/19954153
