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3 years ago

Please someone help me please

Mathematics

2 answers:

gogolik [260]3 years ago

7 0

Answer:

Step-by-step explanation:

take 56 degree as reference angle

using cos rule

cos 56=adjacent/hypotenuse

0.55=12/x

x=12/0.55

x=21.81

x=21.8

pickupchik [31]3 years ago

3 0

Answer:

x = 21.46

Step-by-step explanation:

$cos 56 = \frac{adjacent}{hypotenuse} = \frac{12}{x}\\\\x = \frac{12}{cos 56} = 21.46$

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For a given function f(x), the domain is (-[infinity],-2] and the range is (5,[infinity]). What is the correct domain and range

Serga [27]

Answer:

Domain of the inverse is (5, infinity)

Range of the inverse is (-infinity , -2)

Step-by-step explanation:

To find the domain of the inverse function, we have that;

The range of the function becomes the domain of the inverse

The domain of the function becomes the range of its inverse

so the domain is (5, infinity)

range is (-infinity, -2)

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Step-by-step explanation:

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2 years ago

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3 years ago

Read 2 more answers

Question 1

12345 [234]

Answer:

A). Surface area = 222 cm²

Volume = 180 cm³

B). Surface area = 375 cm²

Volume = 360 cm³

C). % increase in surface area = 67.57%

% increase in volume = 100%

Step-by-step explanation:

In the figure attached base of a prism has been given.

A). Surface area of the prism = (Perimeter of the base of the prism) × height + 2(area of the base)

Perimeter of the base = 5 + 3 + 2 + 2 + 2 + 3 + 5 + 8

= 30

Area of the base = 8×5 - 2×2 = 36 cm²

Surface area of the prism = 30×5 + 2×(36)= 222 cm²

Volume of the prism = volume of the bigger prism - volume of the smaller prism cut off

= 8×5×5 - 2×2×5

= 200 - 20

= 180 cm³

B). Surface area of the prism if it's height is 10 cm,

Surface area = 30×10 + 2×(36) = 372 cm²

Volume of the prism = 8×5×10 - 2×2×10

= 400 - 40

= 360 cm³

C). Increase in surface area = 372 - 222 = 150 cm²

% increase in the surface area = $\frac{150}{222}\times 100$ = 67.57%

Increase in volume = 360 - 180 = 180 cm³

% increase in volume = $\frac{180}{180}\times 100$ = 100%

4 0

2 years ago

You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod

lorasvet [3.4K]

Answer:

a. $y=830*(0.87)^x$

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

$13\%=\frac{13}{100}=0.13$

Upon substituting our given values in exponential decay function we will get

$y=830*(1-0.13)^x$

$y=830*(0.87)^x$

Therefore, the exponential model $y=830*(0.87)^x$ represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

$y=830*(0.87)^2$

$y=830*0.7569$

$y=628.227\approx 628.23$

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be $\frac{830}{2}=415$ .

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

$415=830*(0.87)^x$

Upon dividing both sides of our equation by 830 we will get,

$\frac{415}{830}=\frac{830*(0.87)^x}{830}$

$0.5=0.87^x$

Let us take natural log of both sides of our equation.

$ln(0.5)=ln(0.87^x)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.5)=x*ln(0.87)$

$\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}$

$\frac{ln(0.5)}{ln(0.87)}=x$

$\frac{-0.6931471805599}{-0.139262067}=x$

$x=4.977286\approx 4.98$

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

5 0

3 years ago