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2 years ago

82. A company spends x hundred dollars on an advertising

Mathematics

1 answer:

crimeas [40]2 years ago

5 0

The company spends $649 on advertising

The sales function after advertising is given as:

$S(x) = 5 + 7\ln(x + 1)$

When the total sales is $19,100, we have S(x) = 19100

So, the sales function becomes

$5 + 7\ln(x + 1) = 19.1$

Subtract 5 from both sides

$7\ln(x + 1) = 14.1$

Divide both sides by 7

$\ln(x + 1) = 2.014$

Take exponents of both sides

$x + 1 = e^{2.014$

$x + 1 = 7.49$

Subtract 1 from both sides

$x= 6.49$

Hence, the company spends $649 on advertising

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A piece if wire 40cm is bent to form a right angled triangle whose hypotenuse is 17cm long find the other two sides of triangle

hjlf

Answer: 150mm

Step-by-step explanation:

Take the two adjecent sides of the triangle to be x and y and X is the angle opposite the side, x.

From the trigonometric identities for a right-angled triangle, it is known that

x=170sin X and;

y=170cos X

Thus the perimeter of the triangle is given by

170sin X + 170cos X + 170 = 400

170(sin X + cos X) = 400 - 170

170(sin X + cos X) = 230

sin X + cos X = 230/170 = 1.3529

Squaring both sides hence,

sin^2(X) + 2sin X.cos X + cos^2(X) = 1.8304

Recall that sin^2(X) + cos^2(X) = 1 and 2sin X.cos X = sin 2X.

Thus, the former expression gives;

1 + sin 2X = 1.8304

sin 2X = 0.8304

2X = arcsin (0.8304)

2X = 56.14° or (180 - 56.14)° = 56.14° or 123.86° for X existing within a triangle.

X = 56.14/2 or 123.86/2

X = 28.07° or 61.93°

Thus the two adjacent sides are ;

x = 170 sin (28.07) = 80mm

y = 170 cos (28.07) = 150mm

Using the value of 61.93° as X would give the same values but interchanged for x and y.

I hope you find this useful.

5 0

3 years ago

What are the dimensions of the rectangle shown on the coordinate plane?

sveta [45]

The answer is (+2,6)

4 0

3 years ago

Please help, I will give brainliest, I am struggling badly.

Alja [10]

Answer:

Step-by-step explanation:

Notice they both have the same slope of 3x so they are parallel, but different y intercepts. This means the lines never intersect and thus there are no solutions to the system of equations.

3 0

2 years ago

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If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2

Oksanka [162]

If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width

Solution:

Let the length of rectangle=x

Width of rectangle=x/10

Perimeter is 2(Length+Width)

= 2(x+x/10)

Area of Rectangle= Length* Width=x*x/10

As, Perimeter=2(Area)

So,2(x+x/10)=2(x*x/10)

Multiplying the equation with 10, we get,

2(10x+x)=2x²

Adding Like terms, 10x+x=11x

2(11x)=2x^2

22x=2x²

2x²-22x=0

2x(x-11)=0

By Zero Product property, either x=0

or, x-11=0

or, x=11

So, Width=x/10=11/10=1.1

Checking:

So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2

Area=Length*Width=11*1.1=12.1

Hence, Perimeter= 2 Area

As,24.2=2*12.1=24.2

So, Perimeter=2 Area

So, Answer:Length of Rectangle=11 units

Width of Rectangle=1.1 units

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2 years ago

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omeli [17]

Answer:

a) h'(t)= (6cos3t,-9sin3t,3 $\sqrt[]{5}$ cos3t)

b) t=0.93994736+πn/3

c) Magnitude of h(t) is 3 which is a constant, so h(t) lies on a sphere

Step-by-step explanation:

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3 years ago